Phenomenology of light mesons within a chiral approach

The so-called extended linear sigma model is a chiral model with (pseudo)scalar and (axial)vector mesons. It is based on the requirements of (global) chiral symmetry and dilatation invariance. The purpose of this model is the description of the hadron phenomenology up to 1.7 GeV. We present the latest theoretical results, which show a good agreement with the experiment. In this paper we describe a chiral σ model, called ‘extended Linear σ model (Elσm)’, in which scalar, pseudoscalar, vector, axial-vector quark-antiquark mesons and, in addition, a scalar dilaton/glueball field are the basic degrees of freedom. The aim is to develop a model with the symmetries of QCD which can describe the vacuum phenomenology up to 1.7 GeV. The Lagrangian of the model is built by requiring (i) global chiral symmetry and (ii) dilatation invariance. Although chiral models are studied since long time [1], the here presented Elσm represents the first attempt to treat in a unified chiral framework (pseudo)scalar mesons (including the glueball) as well as (axial-)vector ones. (Previous studies [2] exist only for Nf = 2 and not all the mentioned d.o.f. were taken into account.) It turns out that the inclusion of (axial-)vector d.o.f. has a very strong influence on the overall phenomenology, influencing also the decays in the (pseudo)scalar sector. The explicit form of the Lagrangian in the mesonic sector reads (for a generic number of flavors Nf) [3, 4, 5, 6]: LElσm = 1 2 (∂μG) 2 − Vdil(G) + Tr [ (DΦ)(DμΦ)− aGΦΦ− λ2 ( ΦΦ )2 ] − λ1(Tr[ΦΦ])+ + c1(detΦ † − detΦ) +Tr[H(Φ +Φ)]− 1 4 Tr[L +R] + b 2 GTr[L +R] + 1 2 Tr[δ̂(L +R)]− 2ig2 (Tr[Lμν [L, L ]] + Tr[Rμν [R, R ]]) + h1 2 Tr [ (ΦΦ)(Lμ +R 2 μ) ] + h2Tr [ ΦLμL Φ+ ΦRμR Φ ]